Solveing Linear Systems

[hkus10]

1) Find an equation relating a, b, and c so that the linear system

2x+2y+3z = a

3x- y+5z = b

x-3y+2z = c

is consistent for any values of a, b, and c that satisfy that equation.

what is the method to solve this problem?

 

2) In the following linear system, determine all values of a for which the resulting linear system has

a) no solution;

b) a unique solution;

c) infinitely many solutions:

x + y - z = 2

x + 2y + z = 3

x + y + (a^2 - 5)z = a

 

For these two questions:

Do I make this to be a reduced echelon form first?

If yes, how to make it with some variables a, b, and c?

If no, what is the right approach for this problem?

 

Thanks